The present invention relates to an iterative image reconstruction algorithm, which is a variant of an expectation-maximization (EM) algorithm for computed tomography applied to many applications that include medicine and nondestructive testing. It applies to a variety of types of CT, including transmission CT and emission CT. Transmission CT includes x-ray CT. Emission CT includes positron emission tomography (PET) and single photon emission computed tomography (SPECT).
Computed tomography (CT) is a technique for imaging cross-sections of an object using a series of X-ray measurements taken from different angles around the object. It has been widely applied in diagnostic medicine and industrial non-destructive testing. Two dimensional (2D) and three dimensional (3D) computed tomography are currently used to, e.g., provide defect detection, information about material properties or metrology of manufactured components and materials, such as metal castings.
The expectation-maximization (EM) algorithm refers to variants of an iterative computed tomography (CT) image reconstruction algorithm, first introduced in the 1980's for positron emission tomography (PET). The term EM algorithm strictly refers to the iterative mathematical formalism for defining the objective function and iterative optimization scheme when the data collection system have specific physical characteristics for which a type of Poisson process model is generally appropriate. Strictly speaking, the term EM algorithm applies to many parameter estimation problems and not just CT or PET. Variants to the PET EM algorithm have been designed for single photon emission CT (SPECT), for 2D and 3D deconvolution with light microscopy, telescopic imaging through atmospheric turbulence and general optical imaging deconvolution. With x-ray CT and other forms of transmission tomography there are many forms of iterative reconstruction that are called EM algorithms because they originate from the strict mathematical EM formalism. Even so, some of these so-called EM algorithms have a different form than the one originally developed for PET. In the embodiment described here, the predominant steps in the algorithm were originally designed for PET, even though they are being applied to transmission CT here, but it is still called the EM algorithm here, and perhaps loosely so, because it has resemblance to the same algorithm despite the fact that the physical underpinnings are different.
One historical challenge with the various EM algorithms for CT, and other iterative algorithms, has been long processing times. It is not unusual for the processing time to take on the order of several hours. Accordingly, their use in CT applications has been limited.